From Bachelier to Dupire via optimal transport

Mathias Beiglböck; Gudmund Pammer; Walter Schachermayer

doi:10.1007/s00780-021-00466-3

From Bachelier to Dupire via optimal transport

Mathias Beiglböck, Gudmund Pammer, Walter Schachermayer

Research output: Contribution to journal › Article › peer-review

Abstract

Famously, mathematical finance was started by Bachelier in his 1900 PhD thesis where – among many other achievements – he also provided a formal derivation of the Kolmogorov forward equation. This also forms the basis for Dupire’s (again formal) solution to the problem of finding an arbitrage-free model calibrated to a given volatility surface. The latter result has rigorous counterparts in the theorems of Kellerer and Lowther. In this survey article, we revisit these hallmarks of stochastic finance, highlighting the role played by some optimal transport results in this context.

Original language	English
Pages (from-to)	59 - 84
Journal	Finance and Stochastics
Volume	26
Issue number	1
DOIs	https://doi.org/10.1007/s00780-021-00466-3
Publication status	Published - Jan 2022
Externally published	Yes

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10.1007/s00780-021-00466-3Licence: CC BY 4.0

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From Bachelier to Dupire via optimal transport

Abstract

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